Hello. I believe I can be of help to you with this issue.
Whatever you explain to the kids, your daughter needs to agree with in advance---you need to give the same message simultaneously. I would suspect your daughter feels that you have no good reason to force her out of your home, that she may even feel "entitled" to stay with you and that asking her to leave means you are rejecting her and don't love her anymore. Is this correct?
Before we decide what to say to the kids, can your daughter genuinely understand that your action should help her increase her level of effort and her determination to become more self-reliant and generally, advance her own personal growth and self-care?
Have you given thought to a 2-3 week transition period, in which your daughter would get her own place and move in, but the kids would stay with you for the first couple of weeks while mom acclimated to the idea, the psychological stress
etc., of being "on her own"; after which the additional stress of having the kids would occur when the move in with her. Is this a practical idea, or based on what you know, a good or bad idea?